copyright Jonah Ohayv 7/2002
.... and its following sections
6. http://www.cropcircle-archive.com/intro.html under "Hawkin's theorems"
The "geometrical method" of proof is just our normal logic applied to the comparative relations between the placements and sizes of shapes, between the lengths of straight lines, and so on. Gerald Hawkins, astronomer, has used this geometrical logic to compare the sections of many crop-circles. He's shown that the sizes and locations of the sections in a single crop-circle are often interrelated to each other in the mentioned diatonical ratios. And these fractions, found in the crop formation, can therefore be "translated" to a group of specific musical tones from specific ranges of musical octaves (pitches). In one specific crop-circle formation there may be the equivalents of many different tones, but usually the same few tones or ratios are found several times in the same formation. To see Hawkins' geometrical theorems, method, and examples of crop-circles containing his specific findings, see references numbers 3 and 5, plus Ilyes' summary of them in reference number 4.
For a theoretically profound article, in which crop-circle patterns are put in relationship to the harmonious vibrations of a string - but separated from sounds, including music - read Bert Jansson's contribution in reference number 6.
With a computer-program, one can adjust or compensate for the side-angled views of a crop-circle seen in airplane photos, especially when these photos were taken as close to the formation as possible and as parallel as possible to the field's well-worn tractor paths through the growing crop. One can in this way make new, artificial, computerized photos which show the crop-circle as it would be seen from directly overhead it. With these new photos one can figure out or measure the geometrical comparisions between the crop-circle's sections, and some of these may be diatonic (musical) ratios. Paul Vigay, who's a professional computer expert, has made a method to put these ratios into order, so they end up making a kind of melody.
He's also found another method of comparision, where the computer converts each dot (pixel) in each line of the new computerized photo into a number - probably from the photo's left to right, or top to bottom - and in that sequence, the computer-program (to my understanding) rounds these resulting numbers off to the closest equivalent musical tones. Following this, his program finds a fitting musical key, tempo (speed for playing), and choice of musical instruments for the final musical piece, which is then played and recorded. You'll find Paul's explanation plus an example of his crop-circle music in reference number 8, and information about David Kingston's crop-circle music CDs in reference 9.
Incidentally, to my knowledge, a single song has been recorded about crop-circles. It's called "Corn circles", is in soft-rock style, and is on the CD "Dream Harder" by The Waterboys.
But the question, "How is a sound-vibration or a series of sounds used during the process of a crop-circle's creation?", is different from the question, "Can the harmonic geometrical proportions in the completed crop-circle afterwards be correctly translated into music?" And "Can we get an idea of the crop-circle form's in-built effects on us, by hearing its equivalent music, and feeling what it does to us?"
We all know how a piece of music or even a series of tones can influence our mood, level of energy, feelings, and even body. Just think of the gurgling of stream-water over stones, of your favorite classical music, of loudly played "house" or rock music, or of a physiotherapist's ultra-sound massage apparatus.
The methods of "translating" to crop-circle music are, on the other hand, only in their beginning phase.
A crop-circle has no objective left or right, up or down - that depends on the angle of vision, and each new angle could perhaps represent it's own possible melodies. The musical tune could also be played backwards or "sideways". Even our own written languages proceed in different directions: Hebrew from right to left, Egyptian hieroglyphics (?) from up to down. Also, the order in which the discovered geometrical relations are put is itself variable, and this will give us varying orders in the musical tones.
In addition, we know from the analysis of the straws' overlaying patterns, in crop-circles' where they are laid in layers, that it's highly probable that the sections of a crop-circle are created in some time-sequence of construction-lines, inner-boundary lines, curves, spirals, and so on, which is completely different from our own computer techniques' time-sequence in laying down side-to-side lines of pixel-dots.
The choice of the musical piece's rhythm, intervals, tempo, phrasing, loudness, key, and many other musical dimensions, plus the instruments used, will be based on the composer's/computer programmer's taste and the mood he wants to create, and is not dictated by the crop-circle pattern itself. In a longer piece, any usage of several tones at once (chords) or of new, extra tones will likewise be the composer's decision. Regarding the more mechanical, computer-composing method of converting pixels, how close do the single numbers have to be to actual tonal ratios, to be considered precise enough to make a finished piece of music? And are the rules by which these many numbers are combined inevitable? In summary, as far as I understand these beginning techniques of creation and combination, very many different possible pieces of music could be based on the same geometrical crop-circle pattern.
2. Within a particular formation, we can chant a discovered musical note, in those same sections which give rise to it's ratio. We can gently play a drone instrument like a string-and-bow instrument or didgeridoo in it and see what arises.
3. One could try computing a symmetrical circle's order of musical tones from it's center outwards toward it's farthest perimeter. Of course, many "crop-circles" are in other forms than the circular, and even most "circular" crop-formations are in fact a little elliptical, and have at least one non-symmetrical section.
Can the music's parts be composed in the probable lay-order of the crop-circles' layers and sections, as evinced by the stalk's paths and lay?
4. Some parts of a crop-circle formation are larger or more dominant, and others are more like details. Are some ratios or proportions thereby more dominant or subservient than others? If so, the usage of their equivalent notes in the music should reflect this. At any rate, we can emphasize making the formation's most often repeated ratio the music's key, most repeated note.
5. We should musically try to think in circular patterns, more than in linear ones. And when the formation's symbol makes the visual illusion that it's rotating or 3-dimensional, the music could somehow follow this.
Since a crop-circle is viewed all at once, we can also consider the rather chaotic possibilities of playing the notes simultaneously in several directions at once, rather than from one location to another. What happens if we create 3-D music by playing the various proportions emanating from a section to its neighbors at the same time?
6. In the method of translating a photo's pixels to numbers, how would it sound to play the actual numbers of these vibrations, that is, to make into sounds what is actually found? Instead of translating the numbers into culturally determined musical notes or scales first, which is actually stretching the data to fit a pre-assumed model.
7. Let's start by admitting that a crop-circle tune is one out of many choices, it's an intuition or inspiration, but not "the" rational interpretation instrinsic to that formation. On the other hand, each melody from a specific crop-circle's figured-out relationships is probably a partial truth. If someone then makes several musical variations inspired by the same formation, one might get a many-dimensional theme, with a dominant overall mood. And if several composers made several sets of variations from that crop-circle, we will begin to find possible elements in common.